Bruno Vincent/Getty Images(NEW YORK) -- A young mother whose baby was born with cancer claims that Barclays Capital fired her after an extended leave of absence and cancelled her child's health coverage. Barclays, she says, contested her eligibility for unemployment, forcing her to draw down her savings to support herself and her baby.

Now Rachel Walsh, 32, is filing a complaint alleging breach of contract and gender discrimination, and demanding $10 million in damages and compensation.

Because Walsh waived her right to trial as part of her employment agreement with Barclays, her claim will be arbitrated by FINRA, The Financial Industry Regulatory Authority.

Her attorney, Walker Harman, Jr., of New York says of Walsh's former employer: "I thought surely they would want to settle, because this case has such dramatic and disturbing facts -- and a claimant about whom there are no bad facts."

Walsh graduated from St. John's University in 2004 with a GPA of 3.7. She holds an MBA with a concentration in tax and accounting. According to Harmon, she has never been accused of misconduct.

She started her career at Ernst & Young in 2004, then worked for Merrill Lynch in their global tax department. From there, she says, she was recruited to Barclays in 2010 to be assistant vice president of global finance.

She tells ABC News the hours were sometimes long. When tax deadlines loomed, her day might start at 8:30 a.m. and end at 11 p.m.

She became pregnant late in 2010 -- the same year, according to her complaint, that Barclays gave her a raise, a bonus and a positive year-end review.

Walsh kept working until about three weeks before her due date, when, according to her attorney, her doctor prescribed bed rest because of serious complications with her pregnancy. During that time she was on disability, thus still covered by health insurance.

On May 5, 2011, she gave birth to a son, and began her paid, 12-week maternity leave.

A month later, according to her complaint, her baby was diagnosed with bilateral retinoblastoma -- cancer in the retinas of both eyes. The boy was referred to Sloan-Kettering Cancer Center for treatment.

Walsh says she informed Barclays about her son's cancer. She kept them posted on his progress and asked that she be allowed to take additional leave time, following the expiration of her maternity leave. Barclays agreed to additional unpaid leave, Walsh insists.

Under the Family and Medical Leave Act of 1993, eligible employees of covered employers are entitled to 12 workweeks of leave in a 12 month period if they need the leave to give birth to a child, care for a newborn, or to care for a child with a serious health condition. Walsh's attorney does not contend that Barclays failed, in Walsh's case, to honor that requirement.

At first, says Walsh, her superiors sounded understanding and supportive. She was told, she says, that the bank would have a position for her when she was able to return, and that she could then begin by working from home or on a flexible schedule. She and Barclays signed a contract to that effect, according to her complaint.

Her son's chemotherapy wrapped up in the spring of 2012, and, in early August, she told Barclays she was ready to resume work -- on a flextime basis, if possible.

One of her bosses told her that she (the boss) opposed Walsh's going back into the same position she had held before, owing to the heavy workload and deadlines associated with it. "She said she would not feel comfortable because of nights where I might have to be at the hospital with my son."

This impressed Walsh as sexist.

"She was assuming that because I was the mother," she explains, "I would be the one who would have to sacrifice; that I would not be able to come to work. But if I had been a man, I don't think my boss would have assumed that. Actually, my fiancée had taken a flexible job, so that he could be there for the baby."

This turn of events left Walsh very upset. Desperate to work, according to her complaint, she told Barclays she would go into any position the bank could find for her. The bank eventually responded that no position -- either part-time or full-time- -- were available, and that Walsh was no longer a "fit" for the group with whom she used to work.

Barclays, Britain's No. 2 bank, has been in the spotlight for its role in the interest-rate rigging scandal that allegedly had bankers conspiring to report false lending rates for an index known as Libor. More than $1 trillion in mortgages are tied to the rate. Last year, the bank was fined $360 million by US regulators for its role in the scheme. A day later, CEO Bob Diamond resigned his post.

Barclays, responding to a request for comment from ABC News, says in a statement: "Barclays is committed to working with its employees to accommodate health and family needs that may arise, including accommodating leaves of absence for pregnancies and child care. Ms. Walsh requested, and Barclays approved, several requests for extended leave -- beyond the time periods that would be required by law. During her extended leave, Barclays provided Ms. Walsh and her family continued health coverage benefits. Thereafter, Ms. Walsh declined to return to a full-time position that the firm had available for her."

Attorney Harman says Barclays' assertion that Walsh declined a full-time position is "patently untrue," and that he has recordings to prove it.

Walsh, he says, recorded phone conversations with Barclays HR personnel in which they state not just that no full-time position is available, but that no position at all is available. "They offered her nothing, and told her nothing was available. I have concrete evidence of that," he says.

Walsh exited the company Sept. 6. From the beginning of her maternity leave until then, Barclays had continued paying a portion of Walsh's health insurance.

She managed to get replacement health coverage for her son via COBRA, but at cost to her of $1,800 a month. "With no income, that was very difficult." When she applied for unemployment insurance, Barclays contested her eligibility, though eventually she got it.

Asked how she has paid her bills since leaving the bank, she says, "I've been living off my savings. Before this, I'd been saving for the down-payment on a home. I exhausted that, but I've had help from my family. And my fiancée has helped."

How's her son? "He's doing well," Walsh says. "He's 20 months old now. He's got a checkup tomorrow. He has to be treated every two weeks." The form of pediatric cancer that he has is fast-growing initially but slows with age. By age 7, she says, her son ought to be cancer-free. "He's been through a lot," says the mom. "He started chemo at 7 weeks old. But he's very strong, very tough. We'll get through it."

As for what the future holds for Walsh herself, she tells ABC News: "As far as work, I've been looking. I put a lot of hours into my career, trying to get ahead. Hopefully I can continue."